Above and beyond specific chemical reactions, there are some purely theoretical based on the underlying structure of the chemical network. Kauffman's autocatalytic sets, mentioned above, is one such example, but there are many others. Unfortunately, as Athel Cornish-Bowden points out, most of the researchers in the field have been academic loners, rarely citing each other's work. An excellent review of the history of this subject area is From L'Homme Machine to metabolic closure: Steps towards understanding life by Letelier, Cardenas and Cornish-Bowden.
In brief, these authors give a short history of the underlying metaphors used to develop and frame our understanding of how life works: from late 18th century of a mechanical understanding (think clock), through molecular biology, and finally to systems biology. One central theme underlying almost all of the various "modern" theories is that of metabolic closure, i.e. all of the essential components of an organism are required for the synthesis of all of the other essential components and itself. This self-referential property of living systems is to my mind the thorniest problem confronting theoretical biology (shades of GEB).
The following is a brief synopsis of several theories being bandied about. One of the problems with reading the different authors is that a coherent language of this subject has yet to evolve. Thus, the authors use different words for the same concept and the same words for different concepts. Often these words are different from how biologists use them. This is not meant as a critisism of the authors, since they come from very diverse backgrounds.
(M,R) systems - This theory was developed by Robert Rosen, a mathematician who had a life-long interest in biology. As a graduate student, he and Nicolas Rashevsky developed an approach they referred to as relational biology emphasizing topology over molecular details. From this, Rosen went on to develop his (M,R) systems theory. His theory was developed within the mathematical confines of category theory and was thus beyond the comprehension of most biologists. Recently, Cornish-Bowden and coworkers have translated the essential arguments into set theory
Originally, the "M" stood for metabolism and the "R" stood for repair. Since these words have specific meanings in current molecular biology, C-B has suggested replacement as a more appropriate word that is closer to the underlying meaning within the system. Metabolism is represented as a mapping of substrates to products in the broadest sense, i.e. every molecule within a living organism is a product of metabolism. A subset of these products act as catalysts that are responsible for all of the reactions (mappings). Replacement is more abstract. It is a subset of catalysts that are required for the replacement of catalysts lost due to degradation, inactivation, or dilution because of growth.
Translation of these concepts to biological systems is a daunting task since even the simplest extant systems are extremely complex. A few toy models have been developed to aid in the understanding of these concepts. Regardless, one key aspect from the study of these systems is that they are not hierarchical. Hierarchy is important for understanding subsystems (e.g., gene expression), but for origin of life theories, one can never lose sight of the properties of the whole system.
Autopoiesis - This theory has a rather circuitous route of development. The original theory was developed by Humberto Maturana in the late 1960s and early 1970s. It was developed from using cybernetics to understand the functioning of the brain (modelled after a computer) and an attempt to model the Chilean economy. Maturana came to the conclusion that the brain/computer metaphor was seriously flawed due to the strict input -> output nature of the computer metaphor. Instead, he hypothesized that systems involved in perception/response were always active and constituted a continuous loop. Although different in origin, autopoiesis has many of the same concepts and properties as (M,R) systems.
The chemoton - This is a system of a model organism proposed by Tibor Ganti and published mostly in Hungarian, though an English book was published in 2003, The Principles of Life (Oxford Univ Press). This model provides an outline of a fully functional cell with the incorporation of metabolic, informational, and structural systems. I have not read the book, but Letelier et al. point out that catalytic cycles are a major feature this model.
The hypercycle - Extant organisms have large genomes that specify enzymes that replicate and repair the genome. Obviously, early in the development of life, the enzymes and genomes were much smaller and simpler. The problem with this is that replicating a genome of a decent size requires a low enough error rate to avoid error catastrophy. Maynard Smith and Szathmary coined this Eigen's paradox. Manferd Eigen and Peter Schuster proposed a hypercycle to deal with this problem. This cycle consists of a set of RNA molecules each specifying the synthesis of an enzyme that replicated an RNA molecule different from the one that encoded it. Their analysis suggested that different hypercycle quasispecies could occupy the same space and evolve by Darwinian selection.
Autocatalytic sets - Freeman Dyson and Stuart Kauffman asked the question of what properties were necessary for self organization. Kauffman has pursued this line of reasoning since the mid 1980s. He has always used quirky terms, and in his book The Origins of Order, he refers to this self organization as the Fourth Law of Thermodynamics. I read the book when it first came out, and if one looks more at his arguments than his language, there are many interesting concepts to be examined, from cellular automata to rugged landscapes to gradients in morphogenesis. The basic concept of autocatalytic sets is one of metabolic closure where each metabolite is synthesized by another metabolite in the system. His basic argument is that given enough variety in molecules, some of them will catalyze the formation of other molecules, which in turn catalyze more molecules. From this variety, an autocatalytic set can (will?) emerge and "replicate" itself from the available materials.
Recently Hordijk and Steel have developed Reflexive autocatalytic sets (RAF) to provide a more solid foundation for studying autocatalytic sets. One important contribution is the development of an algorithm to generate these sets, making them amenable to analysis on a computer.
Metabiology - A relative latecomer (not mentioned in this review) is Gregory Chaitin, a mathematician, recently published a book, "Proving Darwin: Making Biology Mathematical". It's on my reading list, but from what I can gather it is about studies that grew out of evolution of LISP programs. Could be an interesting read.
None of the above models are complete and each have their deficiencies/problems as outlined in more detail in the review. Yet, each has contributed valuable concepts and ideas. I must admit that I have been strongly influenced by the writings of Cornish-Bowden. I first encountered his work in basic biochemistry and learned Metabolic Control Analysis from his writings (along with a bunch of others). I look forward to getting the new edition of his textbook, Fundamentals of Enzyme Kinetics, which is now affordable ($63 as opposed to the previous edition at ~$500).
For those who want to read more, the bibliography of the Letelier et al. paper is extensive. For those not familiar with finding non-paywalled papers, Google Scholar is a great resource with links to ungated pdf versions, plus a whole lot more.
Obviously, there is much more on the wet bench side of things along with more specific proposals involving biochemical and organic reactions.